This is the 17140th most frequent Russian word.
старой
"Staroy" means "old" (feminine form).
'старой' functions as an adjective in the genitive case agreeing with the feminine noun 'бабушки'.
Я нашёл книгу старой бабушки.
I found the old grandmother's book.
'старой' functions as an adjective in the prepositional case modifying the feminine noun 'комнате'.
В старой комнате пахнет свежей краской.
In the old room, there is a smell of fresh paint.
'старой' is used as a predicate adjective in the instrumental case following the verb 'стала' to describe the state of the subject.